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Fence posts problem

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Fence posts problem

by akshatgupta87 » Sun Jun 26, 2011 10:23 am
Q.) A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts
along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would
surround this pasture if the width were doubled? (Assume that the space taken up by the fence posts is
negligible.)
A) 14
B) 16
C) 20
D) 22
E) 24

Someone explain.
Thanks,
Akshat
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by MBA.Aspirant » Sun Jun 26, 2011 11:15 am
Q.) A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would surround this pasture if the width were doubled?

I'm getting 13 for this.

Length = 5*15 = 75

Width = 240 - (2*75) /2 = 45

Width doubled = 90

so along the width = 90/15= 6 +1 = 7 posts
along the length = 75/15 = 5 +1 = 6

Total = 7+6 = 13

Where did I go wrong?
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by akshatgupta87 » Sun Jun 26, 2011 11:34 am
OA is D
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by anuragvaid » Mon Jun 27, 2011 2:01 am
Length = 5*15 = 75 Width = 240 - (2*75) /2 = 45 Width doubled = 90

so along the width = 90/15= 6 +1 = 7 posts

along the length = 75/15 = 5 +1 = 6

U are correct till here....Now simply we have, 12 fences along the length which also includes the four corners.

Along the breadth, we have 7 or 14 on both sides, but this again includes the four corners. So, removing those 4 (since those are already counted for in Length), we are left with 10 along the breadth.

Adding the two ; 12+10 = 22. Option D.

Anurag
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by Sci45 » Thu Aug 10, 2017 7:09 pm
anuragvaid wrote:Length = 5*15 = 75 Width = 240 - (2*75) /2 = 45 Width doubled = 90

so along the width = 90/15= 6 +1 = 7 posts

along the length = 75/15 = 5 +1 = 6

U are correct till here....Now simply we have, 12 fences along the length which also includes the four corners.

Along the breadth, we have 7 or 14 on both sides, but this again includes the four corners. So, removing those 4 (since those are already counted for in Length), we are left with 10 along the breadth.

Adding the two ; 12+10 = 22. Option D.

Anurag
Where do these numbers come from?
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by regor60 » Fri Aug 11, 2017 6:57 am
Along the length there are 6 posts. Recognize that means a post at each end and 5 intervals of 15 feet to span the 6 posts.

So, the length is 5 x 15 or 75 feet. Given that the perimeter is 240 feet, the widths contribute 240 -(2x75) or 90 feet to the perimeter, meaning that the width is 45 feet.

Doubling the width therefore means the width ( now length) is 90 feet and the length (now width) is 75 feet.

Remembering from above that there is one more post than interval along a dimension there are 90/15 + 1 or 7 posts along the new length, or 14 in total for both lengths.

Likewise, along the 75 foot width, there are 75/15 +1 posts or 6.

HOWEVER, recognize that the two end posts of the width were already accounted for in the 14 determined above. So the number of INCREMENTAL posts along the width is 2 x (6-2) or 8.

Adding the posts along the length, 14, to the other posts along the width, 8, yields22
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by Matt@VeritasPrep » Fri Aug 18, 2017 2:27 pm
One of the keys here is that every corner post is counted TWICE, since it's effectively a vertex of the rectangle. The other key is that a side with 6 posts really has 5 fencelengths of 15, since we only need 1 fence to connect 2 posts, 2 lines to connect 3 posts, etc.
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Re: Fence posts problem

by Scott@TargetTestPrep » Sun Feb 16, 2020 7:45 am
akshatgupta87 wrote: ↑
Sun Jun 26, 2011 10:23 am
 Q.) A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts
along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would
surround this pasture if the width were doubled? (Assume that the space taken up by the fence posts is
negligible.)
A) 14
B) 16
C) 20
D) 22
E) 24

Someone explain.
Thanks,
Akshat
Since there are 6 fence posts along the length of the pasture, there are 5 spacings between the posts. Therefore, the length is 5 x 15 = 75 feet, and the width is (240 - 75 x 2) / 2 = 90/2 = 45 feet. We are told to double the width, sothe new width is 90 feet, and there will be 90/15 + 1 = 7 posts along the new width.

The two lengths of the new pasture have 6 x 2 = 12 posts, and the two widths have 7 x 2 = 14 posts. However, we double counted the 4 corner posts. Therefore, the total number of posts around the new pasture is 12 + 14 - 4 = 22.

Answer: D

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